Capability complements experimental probes

Exploring metal-ligand interactions in actinide complexes using density functional calculations

Modern quantum chemistry techniques can provide insights into electronic properties of actinide complexes such as the nature of the chemical bonding, the structures and relative energies of related compounds, and the nature of electronic excited states. The results are obtained from quantum mechanical calculations that treat the interactions of the electrons with the nuclei in the molecule. From the solution of the molecular Schröedinger equation, wave functions can be obtained that describe the electrons, and, in turn, the overall electronic density in the molecule.

The ability to perform reliable calculations on actinide species is a result of several developments over many years, including theoretical methods and increasing computational capabilities. In particular, recent advances in density functional theory (DFT) have made possible calculations on large chemical systems compared to conventional quantum chemistry approaches.

Calculated structures for [UO₂(H₂O)₅] ²⁺ (left) and [(NpO₂)(crown)]⁺ (right) complexes from density functional theory calculations are shown at right. The figure on the left is a typical example of an actinyl species comprised of a linear bonding linkage (the central O–U–O molecule) that is coordinated with five molecules of water bound to the actinide atom in the central plane (U=blue, O=red, and H=white). The figure on the right shows a recently identified organic ligand known as a crown ether—the structure encircling the neptunium molecule (Np=blue, O=red, C=grey, and H=white).

Another development involves techniques to treat just the valence electrons (those in the outermost "shells" of atoms that are most likely to participate in the formation of chemical bonds) in molecules containing heavy elements such as actinides. In addition, these approaches simultaneously incorporate the effects of relativity on the valence electrons, since relativistic effects are crucial in this region of the periodic table.

Oxo complexes as testbeds

Among the most prevalent motifs in the chemistry of higher-valent actinide species are actinyl species comprised of a linear bonding linkage [O=U=O]²⁺ as in the uranyl (UO₂²⁺) species that generally coordinates to other molecules (ligands) by forming bonds around a central plane about the O and U. Typical examples are the aquo complex [UO₂(H₂O)₅] ²⁺ and its Np and Pu counterparts that represent the dominant species found in aqueous solution at low pH for the +5 and +6 oxidation states of the actinides. Recent calculations have examined how the molecular structures and calculated vibrational frequencies of the O=An=O²⁺ unit systematically vary across the actinides from U to Np to Pu.

These two organoactinide species illustrate the role density functional theory plays in understanding bonding in the actinides. The top left figure is the calculated structure of the U(VI) complex Cp*₂U(NPh)₂, which has no unpaired electrons. The top right figure is the calculated structure of the U(IV) complex Cp*₂U(CH₃-N-N-CR₂)₂, which has two unpaired 5f electrons. The lower left figure is a contour plot of one of the valence orbitals in Cp*₂U(NPh)₂. The lower right figure is a contour plot of a similar orbital in Cp*₂U(CH₃-N-N-CR₂)₂. The blue and red indicate positive and negative contours, respectively. The larger amount of participation by the U atom in the bonding for the complex on the left is indicated by the relatively larger proportion of contours on the metal relative to the N-containing ligands. By contrast, for the complex on the right, a larger proportion of the contours is found on the N-containing ligands.

These predictions can be compared with data from experimental probes in solution such as XAFS and Raman spectroscopy. Both theory and experiment give the same values for the axial An=O bond length in this series in going from U (1.76 Å) to Np (1.75Å) to Pu (1.74 Å). The calculated Raman frequencies of the O=An=O²⁺ unit are decreasing from 908–805 cm^-1, which may be compared with the observed experimental range of 872– 835 cm^-1 across the same series. The calculated bond length between the actinide and the equatorial oxygen atoms (2.52 Å) is somewhat longer than observed by XAFS (2.42 Å).

In addition, solvent effects, which are crucial for predicting reaction energies in solution, can be included by an effective medium model that includes a polarizable dielectric medium surrounding the molecule (for example, water or an aqueous solution of sodium chloride).

One of the challenges in environmental chemistry of actinides has been to characterize and selectively remove such species from waste streams, in chemical processing, or in geochemical formations. Our synthetic chemistry colleagues at Los Alamos recently identified an organic ligand known as a crown ether that binds to the Np(V) oxidation state of neptunyl to form a [(NpO₂)(crown)]+ complex.

The calculated structure from density functional calculations is in good agreement with the crystal structure obtained experimentally. The calculations give a good prediction of the Raman frequency for the O=Np=O vibration (776 cm^{-1 calculated, 780 cm-1 experimental), the predicted Np–O bond length (1.81 Å calculated, 1.80 Å experimental), as well as other structural features.}

The only other analogous compound synthesized to date contains the UO₂ ²⁺ group. Calculations have been performed for the entire series of complexes for both +5 and +6 oxidations states of U, Np, and Pu for the [AnO₂(crown)]^q+ species. For most cases the calculations represent predictions where experimental species have not been isolated to date. This illustrates how theory can complement experimental probes to help identify and characterize actinide species of potential environmental interest that may be difficult to isolate or study experimentally.

Understanding bonding and reactivity

Among the novel features of actinide chemistry is the ability of these complexes to involve both 5f and 6d orbitals in forming chemical bonds. In the actinide series, proceeding across the periodic table entails formally filling up the 5f shell. The neighboring 6d shell is also energetically accessible, and this shell even lies lower in energy than the 5f shell in the early actinides. The principal means by which theory can provide an understanding of the bonding in this actinide series comes from examination of the molecular orbitals. These are the one-electron wave functions for individual electrons in the molecule in the DFT calculations, from which the total electron density for the molecule ultimately is obtained.

Two representative organoactinide species illustrate the role of theory: the bis(imido) U(VI) complex Cp*₂U(NPh)₂ and the bis(hydrazonato) U(IV) complex Cp*₂U(CH₃-N-N-CR₂)₂. In the calculations, a Cp group (C₅H₅) was used to model the permethyl cyclopentiadienyl group, C₅Me₅ (Cp*) as shown in the figure. For more information on the synthesis of these compounds, see the article on page 23. The U(VI) complex has no unpaired electrons, while the U(IV) complex has two unpaired 5f electrons. The molecular orbitals describing the other valence electrons can be viewed as arising primarily from the ligands bound to the uranium with some participation by the uranium orbitals. DFT calculations have been performed on both complexes to examine the nature of the bonding, geometrical structure, and thermochemistry of these complexes. It is often useful to examine the spatial nature and relative energies of the molecular orbitals to understand chemical bonding as well as to explain electronic spectroscopy. In the Cp*₂U(NPh)₂ complex, the energy levels of the ligands themselves are stabilized by interactions with 6d and 5f orbitals from the U. The energy levels correspond physically to the binding energy needed to remove or excite an electron at a particular energy, since in quantum theory, the molecular energy levels have discrete values.

This schematic diagram of Cp*₂U(NPh)₂ shows the interaction of ligand orbitals (on the left) with 6d and 5f orbitals of U (on the right) to form the molecular orbitals in the U complex (in the middle). The vertical scale corresponds to the energy needed to remove an electron from a particular filled orbital (electrons are indicated by arrows) and excite it to an empty orbital, as occurs when the molecule absorbs energy in the visible or UV region of the spectrum.

In visible and UV spectroscopy, the incident light excites an electron from a filled to an unfilled level as indicated by the arrow. In photoelectron spectroscopy, higher energy x-ray sources are used to ionize the molecule by completely ejecting an electron from the different energy levels.

If the ligands had their formal charge (such as –1 for Cp*, –1 for hydrazonato and –2 for imido) the U atom in turn would have +6 and +4 charges associated with its formal valence in the two molecules. The calculations show this ionic picture to be too extreme, since the DFT results give significantly reduced charges on the uranium of only +1.0 and +1.3 for the U(VI) and U(IV) complexes, respectively.

When all of the bonding electrons are included, this analysis also shows a net "population" of 2.2 6d electrons and 2.5 5f electrons for the U(VI) complex compared to 1.6 6d electrons and 0.8 5f electrons for the U(IV) complex, to which must be added the two nonbonding 5f electrons for a total 2.8 5f-electron population.

A large portion of the metal's participation in the bonding can be traced to a few key orbitals in each system. Two representative orbitals that are qualitatively similar looking are shown in the panels in the figure on page 12. The orbital on the left in the bis(imido) complex has substantial U involvement (35% 5f of the overall orbital containing a pair of electrons) compared to only 11% 5f involvement in the bis(hydrazonato) complex. This translates into greater covalent bonding interactions (in fact multiple-bonding character) in the bis(imido) complex.

While these aspects are beyond the scope of this discussion, it is informative to consider the electronic spectroscopy of these molecules in terms of excitations from these bonding orbitals to unfilled orbitals. If the unfilled orbitals correspond to 5f or 6d metal orbitals, they would be denoted as charge-transfer excitations compared to ligand-based excitations if both pairs of orbitals reside on the ligand. In addition, as in the case of the U(IV) complex with a 5f2 configuration, there are also low-lying excitations arising from filled to unfilled 5f excitations that give rise to the absorption spectra in the visible and near-IR region. Finally, the energies and orbital makeup of the occupied levels can be used to compare with photoelectron spectra that probe the molecular binding energies.

These examples serve to show how DFT electronic structure calculations can be used to calculate molecular structure and spectroscopic properties of actinide complexes. The close agreement between theory and experiment for known compounds gives us reasonable confidence in our ability to use DFT theory to predict properties of compounds that have not yet been prepared and provides valuable insight and guidance for interpreting the nature of covalency and chemical bonding and interpretation of spectroscopic properties.

The research on aqueous complexes was upported by a Laboratory Directed Research and Development (LDRD) project administered by the Glenn T. Seaborg Institute at Los Alamos National Laboratory. The organoactinide research is suppported by the DOE Office of Basic Energy Sciences.

This article was contributed by Los Alamos researchers P. Jeffrey Hay and Richard L. Martin of the Theoretical Division.

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